Interesting, I hadn't heard of an Einstein tile before! Apparently a tile was just found that is an Einstein tile: https://www.livescience.com/newly-discovered-einstein-tile-is-a-13-sided-shape-that-solves-a-decades-old-math-problem

Also, I had written before about tilings, and in particular in the context of quasicrystals: https://peakd.com/hive-128780/@mes/quasicrystals-penrose-tilings-metamaterials-and-optical-cloaking